The badge is a United Confederate Veterans anuual reunion/convention badge, dating from sometime between 1867 and the 1930s. If you want a specific date, you'd have to do some research on what years the UCV annual convention was held in New Orleans.
Your two buttons showing an eagle standing on an anchor are not actual US Navy buttons, but instead are imitations manufatured for use on civilian-clothing, known as Fashion buttons.The small button saying "City of New Orleans" on its front is most probably a Police button from that city, but may have been worn by some other type of city-employee there.
Your other two buttons (showing a spread-winged eagle with a long ribbon in the eagle's beak are US Army "Great Seal" buttons, which date from 1902 to the present. More specifically, the one which has "black finish" on it dates from around World War One to a few years afterward. The other one, without black-finish, dates from the 1920s onward. If you can tell us the name in the backmark (maker's-mark) on their back, we might be able to narrow down their time-period.